Question

Will give brainliest

Answer 1

Step-by-step explanation:

Step 1:  Answer question 1

$(x + 1)^2 + (y + 8.75)^2 = (y + 9.25)^2$

      $x^2 + 2x + 1 = 2y + 9$

What we are doing in this problem, is that we are squaring both sides in order to help simplify.  Number 1 has the second option or B.

Step 2:  Answer question 2

$\sqrt{(x + 1)^2 + (y + 8.75)^2}$

What we are doing is that we are finding the distance from the point on the parabola to the directrix.  Number 2 has the last option or F.

Step 3:  Answer question 3

Use (x, y)

What we are doing is that we are finding a point on a parabola.  Number 3 has the fifth option or E.

Step 4:  Answer question 4

$y = \frac{1}{2}x^2 + x - 4$

What we are doing is that we are writing the equation of the parabola.  Number 4 has the third option or C.

Step 5:  Answer question 5

$\sqrt{(x + 1)^2 + (y + 8.75)^2} = \sqrt{(y + 9.25)^2}$

What we are doing is that we are setting the distance from focus to the point equal to the distance from directrix.  Number 5 has the first option or A.

Step 6:  Answer question 6

$\sqrt{(y + 9.25)^2}$

What we are doing is that we are finding the distance from the point on the parabola to the directrix .  Number 5 has the fourth option or D.

Answer 2

hope this helps

1-use (x-y) =  set the distance from focus to the point equal to the distance from directrix to the point

2-$\sqrt{(x+1)^{2}(y-2)^{2}$ = square both sides and simplify equation

3-$\sqrt{(x-5)^{2} }$ =choose a point on the parabola

4-$\sqrt{(X-5)^{2} }$4- $\sqrt{(X+1)^{2}+(Y-2)^{2} } =\sqrt{(X-5)^{2} }$ = =find the distance from the focus to the point of the parabola

5-$(X+1)^{2}+(Y-2)^{2}=(X-5)^{2}$ =write the equation of the parabola

$Y^{2} -4Y+4=-12X+24$  

6-$X= -\frac{Y^{2} }{12}+\frac{Y}{3}+\frac{5}{3}$ =find the distance from the point of the parabola to the directrix